Topics in general relativity theory : gravitational-wave measurements of black-hole parameters; gravitational collapse of a cylindrical body; and classical-particle evolution in the presence of closed, timelike curves

Abstract

In this thesis I present three separate studies on three different topics in General Relativity.
The first study investigates the accuracy with which the mass and angular momentum of a black hole can be determined by measurements of gravitational waves from the hole, using a laser-interferometer gravitational-wave detector. The black hole is assumed to have been strongly perturbed, perhaps by coalescence with a binary companion, and the detector measures the waves produced by its resulting vibration and ring-down. The uncertainties in the measured mass and angular momentum arise from the unavoidable presence of noise in the detector. It is found that the faster the hole rotates, the more accurate the measurements will be, with the uncertainty in the angular momentum decreasing rapidly with increasing rotation speed. It is also found that the errors in the mass and angular momentum are highly correlated.
The second study is an analysis of the gravitational collapse of an infinitely long, cylindrical dust shell. This analysis is expected to be helpful in understanding the behavior during collapse of more realistic, finite-length bodies. It is found that the collapse evolves into a naked singularity in finite time, as measured by a distant observer or by one riding on the shell. Analytical expressions for the variables describing the collapse are found at late times, near the singularity. The picture is completed with a numerical simulation that follows the collapse from the start until very close to the singularity. The singularity is found to be strong, in the sense that an observer riding on the shell will be infinitely stretched in the direction parallel to the symmetry axis, and infinitely compressed in the azimuthal direction. The gravitational waves emitted from the collapse are also analyzed.
The last study focuses on a different kind of phenomenon, namely, the consequences of the existence of closed timelike curves in a spacetime that contains a wormhole. One might expect that the closed timelike curves would cause difficulty for the initial value problem for systems that evolve in such a spacetime: a system with apparently well-posed initial conditions might have no self-consistent solutions to its evolution equations. We study the simple case of a macroscopic, classical particle with a hard-sphere potential (a "billiard ball"), and we focus attention on initial conditions for which the evolution, if followed naively, is self- inconsistent: the ball enters one mouth of the wormhole and then comes out of the other mouth at an earlier time, then collides with its younger self, preventing itself from ever entering the first mouth. We find, surprisingly, that for all such "dangerous" initial conditions, there are an infinite number of self-consistent evolutionary solutions, involving a glancing collision and any number of wormhole traversals. We also find that for many non-dangerous initial conditions, there also exist an infinity of possible evolutions.